خوشه بندی نوسانات، اثر اهرم، و پرش پویایی در ایالات متحده و در بازارهای سهام حال ظهور آسیا

This paper proposes asymmetric GARCH-Jump models that synthesize autoregressive jump intensities and volatility feedback in the jump component. Our results indicate that these models provide a better fit for the dynamics of the equity returns in the US and emerging Asian markets, irrespective whether the volatility feedback is generated through a common GARCH multiplier or a separate measure of volatility in the jump intensity function. We also find that they can capture several distinguishing features of the return dynamics in emerging markets, such as, more volatility persistence, less leverage effects, fatter tails, and greater contribution and variability of the jump component.

Mixed GARCH-Jump modeling has emerged as a powerful tool to describe the dynamics of asset returns in discrete-time. Recent work in this area by, for example, Duan et al., 2005, Duan et al., 2006 and Maheu and McCurdy, 2004 allows for time-variation in the jump component of the mixed GARCH-Jump model. In particular, Duan et al. develop a constant intensity NGARCH-Jump model that allows for time-variation through a common GARCH multiplier in the “diffusion” and jump component.1 In the limit, their discrete-time model can converge to continuous-time jump-diffusion processes with jumps in the stochastic volatility. They find that the NGARCH-Jump model provides a better fit for the time-series of S&P 500 index returns relative to the normal NGARCH specification. Maheu and McCurdy develop a mixed GARCH-Jump model that admits separate time-variation and clustering in the jump intensity, but does not accommodate for volatility feedback in the jump component. When applied to individual stocks and indices in the US, their model outperforms the GARCH-Jump model with constant intensity and i.i.d. jump component. These findings give rise to the question which jump structure best fits the asset return dynamics under an asymmetric GARCH specification. Is it volatility feedback in the jump component, autoregressive jump intensity, or a combination of both? Should volatility feedback in the jump component be generated through a common GARCH multiplier or a separate measure of volatility in the jump intensity function? To answer these questions, we propose asymmetric GARCH-Jump models that synthesize autoregressive jump intensities and volatility feedback in the jump component. We offer two extensions of the existing GARCH-Jump models. First, we extend the constant intensity asymmetric GARCH-Jump model in Duan et al., 2005 and Duan et al., 2006 by accommodating for time-varying, autoregressive jump intensity. This extension allows for two sources of time-variation in the jump component, namely, the common GARCH multiplier and the separate autoregressive arrival rate of jumps. Each factor affects the variation in jumps in a different way. The common GARCH multiplier induces time-variations in the jump component that are synchronous with the diffusion component, making these two components inseparable. In contrast, the autoregressive intensity allows the probability of jumps to change over time and can generate variations in the jump component that are fully separable from the diffusion component. Second, we extend Maheu and McCurdy (2004) specification by allowing the jump intensity to be a non-affine function of the return volatility or its proxy. Studies in the continuous-time literature by Bates, 2000, Duffie et al., 2000 and Pan, 2002 point to the importance of incorporating volatility in the random jump intensity. They show that a high volatility before and during a market crash can increase the probability of jumps. Chernov et al. (1999) observe, however, that the return volatility tends to remain high after a market crash, while the arrival of jumps drops considerably after a crash. To accommodate both relationships, we use the absolute value of the equity returns as a measure of return volatility since it permits the jump intensity to be a non-affine function of the volatility. In this extended model, the GARCH multiplier is a scale factor for only the diffusion component and the contribution of each component is fully separable. As in Duan et al., 2005, Duan et al., 2006 and Maheu and McCurdy, 2004, our extended GARCH-Jump models incorporate jumps in the returns and volatilities. The inclusion of jumps in the volatility can potentially account for the large, but persistent movements in the emerging market volatility. The models allow conditional volatility to respond asymmetrically to both normal innovations and jump shocks. They can therefore accommodate both positive and negative correlations between the asset returns and volatilities. The main difference between the extended models is the way they allow for volatility feedback in the jump component. We compare these models to examine whether volatility feedback through a common GARCH multiplier or a separate measure of return volatility in the jump intensity is more appropriate to describe the return dynamics. In addition, this paper investigates whether the proposed GARCH-Jump models can capture the distinguishing features of return dynamics in the emerging equity markets. As documented in the literature, equity returns from emerging markets exhibit different characteristics compared to those from developed markets. For example, Harvey, 1995 and Bekaert and Harvey, 2002 argue that emerging market returns have higher volatility, fatter tails, and greater predictability. In contrast to the mature markets, Bekaert and Harvey (1997) show that volatilities in emerging markets are primarily determined by local information variables. Aggarwal et al. (1999) find that the volatilities in emerging markets exhibit large and sudden shifts. They find that these jump-like changes in the emerging markets’ volatility are primarily associated with important local events. Aggarwal et al. also find that most emerging markets’ returns show positive skewness, which is in contrast to the negative skewness in developed markets. We therefore apply our models to daily index returns in both the US and Asian equity markets. We select a diversified group of emerging Asian markets, ranging from countries that were severely affected by the 1997 Asian financial crisis to those that were relatively unaffected. We consider a sample period from July 5, 1995 through August 7, 2002, which allows us to examine the dynamics of the Asian equity returns before, during, and after the crisis. To evaluate the contribution of each models’ component, we estimate and test several special cases of the models. The main results can be summarized as follows. Overall, while no one model fits best in all markets, we find that the jump structures with autoregressive jump intensity and volatility feedback in the jump component provide a better fit for the dynamics of the equity returns in the US and most of the emerging Asian markets. The extended GARCH-Jump models outperform the specifications that only accommodate a common GARCH multiplier or autoregressive jump intensity. The rejection of the common GARCH multiplier as the only source of time-variation in both the diffusion and jump component is more evident in the presence of market crashes, pointing thereby toward the need for a separate source of time-variation in the jump component. When comparing the extended models with each other, we find that, on a aggregate level, volatility feedback through a separate measure of volatility in the jump intensity function performs as well as the common GARCH multiplier. However, the results for the individual parameter estimates suggest that the autoregressive arrival rate is more compatible with a volatility feedback through a separate state variable in the jump intensity function than with a common GARCH multiplier. Further, we find that the extended GARCH-Jump models can capture several stylized facts in the volatilities and jump dynamics of the returns in the US and emerging Asian equity markets. The results indicate that the return volatility in these markets is stochastic, persistent, and asymmetric; the volatility persistence in the emerging markets is higher than in the US; the leverage effect is higher in the US; the returns as well as the volatilities exhibit jump discontinuities; volatilities respond asymmetrically to jump shocks in both the US and emerging markets; and jumps play a more predominant role and induce a quite different tail behavior in the emerging markets. The remainder of the paper is structured as follows. In Section 2, we present the extended GARCH-Jump models that allow for volatility feedback and time-varying autoregressive jump intensities. Section 3 presents the data and estimation method. The results are discussed in Section 4 and Section 5 provides the conclusion of the paper.

In this paper, we have proposed several asymmetric GARCH-Jump models that synthesize time-varying autoregressive jump intensities and volatility feedback in the jump component. One is an extension of Duan et al., 2005 and Duan et al., 2006, where volatility feedback is generated by a common GARCH multiplier that induces time-variation in both the diffusion and jump component. This extension allows for two sources of time-variation in the jump component, namely, the common GARCH multiplier and the separate autoregressive arrival rate of jumps. Another extends the Maheu and McCurdy (2004) specification by allowing the jump intensity to be both autoregressive and dependent on the return volatility or its proxy. Hence, the contribution of the diffusion and jump component in the total variation of the equity returns is fully separable. To obtain non-affine jump intensities, we choose the absolute value of the equity return as a measure of return volatility. The extended GARCH-Jump models incorporate jumps in the returns and volatilities, allow conditional volatility to respond asymmetrically to both normal innovations and jump shocks, and generate stochastic volatility from two different sources: the GARCH effects and the arrival rate of jumps. We compare the extended models to examine whether volatility feedback through a common GARCH multiplier in the jump component or a separate measure of return volatility in the jump intensity is more suitable to describe the return dynamics. We estimate several special cases to assess the importance of each model’s component and to determine which jump structure provides the best fit. We also investigate whether the mixed GARCH-Jump models can capture the essential features in the emerging Asian equity markets, covering the periods before, during and after the Asian crisis. We find that the jump structures with autoregressive jump intensity and volatility feedback in the jump component provide a better fit for the dynamics of the equity returns in the US and most emerging Asian markets under consideration. In comparing the extended GARCH-Jump models, the goodness-of-fit tests indicate that volatility feedback through a separate measure of volatility in the jump intensity performs as well as the common GARCH multiplier. The extended GARCH-Jump models can also capture the distinguishing features in emerging equity markets.